We propose the development of a very compact, rotating-wave electron beam accelerator (RWA) for x-ray radiotherapy applications. The proposed accelerator employs a very short accelerating structure to accelerate a low-energy electron beam to a final energy of 6 MeV in a highly efficient manner. The RWA offers twice the efficiency of conventional small accelerators in addition to having a greater degree of simplicity and a more compact design. Based on its high efficiency and compactness, we estimate a reduction in the price of the entire system by a factor of 2. Also since the RWA requires half the electrical power to operate, this should translate to a 50% savings in electrical power costs in the day-to-day operation of the accelerator. Earlier testing of a C-band prototype has successfully demonstrated the operation of this new accelerator where a 3 keV electron beam was accelerated to the goal 800 keV using only 80 kilowatts of power. Our preliminary studies indicate that with a six-inch long cavity we can produce a 6 MeV electron beam using half of the microwave power of that required by state-of-the-art radiotherapy machines. During Phase I we will perform a thorough design of the accelerating cavity and magnetic system that should lead to the construction and testing of a 6 MeV medical accelerator system in Phase II. Once fully developed, the rotating-wave accelerator could be the basis for a new class of very compact 6 MeV radiotherapy accelerators that should be affordable for small clinics and hospitals around the country.